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Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval ? Justify your answer.
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It is not correct because in a histogram, the area of each rectangle is proportional to the corresponding frequency of its class
The mean of a data is \(\bar x \). What will be the new mean if each value of the data is increased by a ?
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Mean
Observe the data : 16, 9, 3, 9, 9, 3, 2. Since, 16 is the highest value in the observation, so the mode of the data is 16. Is it correct ?
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No mode is the number that occur most times. Here mode is 9
What is the median of first 19 natural numbers ?
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First 19 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 19
Median is 10
The mean of 5 numbers is 27. If one of the numbers is excluded, the mean of remaining numbers is 25. Find the excluded number.
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Excluded number
So the excluded number is 35
Find the median of first ten prime numbers.
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First ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Median
The weights, in grams of 30 oranges picked at random from a basket are given below:
70, 110, 119, 81, 158, 144, 125, 120, 155, 90, 102, 62, 98, 156, 145, 150, 135. 140, 82, 125, 61, 85, 117, 121, 121, 130, 65, 69, 92, 100.
Construct the continunous grouped frequency distribution table, width of each class being 20 grams and first class being 60โ80 (80 not included).
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Average monthly consumption of petrol for first 3 months is 86 litres and for next 9 months is 152 litres. Find the average consumption for the whole year.
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Average consumption
The mean marks scored by 100 students was 40 Later on, it was discovered that a score of 53 was misread as 83. Find the correct mean marks.
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Correct mean
Find the mean of 3, 4, 6, 7, 8, 14. If 5 is added to each observation, what will be the new mean ?
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Mean
If 5 is added then new mean
Find the median of data : 26, 56, 32, 33, 60, 17, 34, 29 and 45. If 26 is replaced by 62, find the new median.
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Median
Now
New median
Find the median of the following data : 23, 31, 47, 24, 46, 27, 37, 30.
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Median
The median of the observations \(26, 29, 42, 53, x, x + 2, 70, 75, 82, 93\) arranged in ascending order is \(65\). Find the value of \(x \) :
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A/Q
The following data represents height (in cm) of 20 students of a class : 132, 130, 134, 135, 130, 131, 134, 135, 133, 133, 130, 131, 133, 136, 135, 134, 130, 133, 129, 136.
Make a frequency table for the above information
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The mean of 70 observations was found to be 150. While checking, it was detected that one value 210 was wrongly copied as 140, while calculating the mean. Find the correct mean.
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Correct mean
The class marks of a distribution are 6, 10, 14, 18, 22, 26, 30. Find the class size and the class intervals.
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class size
We subtract from each class mark to get lower limit and add 5 to each class to get the upper limit
The points scored by a basket ball team in a series of matches are as follows :17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28.
Find the median and the mode for the data.
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Median
As 10 occurs most frequently so the mode is 10
Find the mean of the following data :
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The mean of 15 numbers is 9. If each observation is multipled by 4, what will be the new mean?Give reason for your answer.
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Mean of 15 numbers = 9
when each observations is multiplied with 4 then new mean
The mean of 13 observations is 14. If the mean of the first 7 observations is 12, and that of the last 7 observations is 16, find the seventh observation.
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seventh sum of 130 observation
seventh sum of 7 observation
seventh sum of last 7 observation
seventh observation
Observe the following table :
If the mean of the data is 25.75, find the value of p.
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If the mean of five observations \(x, x + 2, x + 4, x + 6, x + 8\) is \(11\), find the mean of first three observations.
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Three observation are
Mean
The following observations have been arranged in ascending order where median of the data is \(63 : 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95\). Find the mean of the data.
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A/Q
observation are
Mean
Find the arithmetic mean of the following table
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Calculate the ariithmetic mean of the following data :
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The mean of 14 values of a data is 23. If one more vlaue is introduced in the data, the mean of 15 values becomes 25. Find the fifteenth value.
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Fifteenth value
The mean of 50 observations of a data was 70. At later stage, it was noted that a value of 85 was wrongly read as 60. Find the value of the correct mean.
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Correct mean
Find the average daily income of the employees of the company.
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Find the mean salary of 50 workers of a factory from the following data.
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The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them in kg are 52, 54, 55, 53, 56, 54. Find the weight of the seventh student.
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Weight of 6 students
weight of 7 students
weight of 7th student
The mean of 25 observations is 36. If the mean of the first 13 observation is 32 and that of last 13 observations is 39, find the 13th observation.
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observation
In a city, the weekly observation made in a study on the cost of living index are given in the following table :
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First we obtain the class marks as given in the following table.
Then, The frequency polygon is as follows
The distance (in km) covered by 20 cars in 2 hours are given below : 125, 120, 130, 134, 100, 90, 96, 100, 110, 120, 112, 116, 104, 96, 100, 98, 120, 122, 124, 92. Represent the data as a continuous frequency distribution table with equal class size, starting from 90 โ 95.
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The following table gives the distribution of students of two sections according to the marks obtained by them.
Represent the marks of the students of both the sections on the same graph by two frequency polygons.
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Obtain the mean of the following data :
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If the mean of the following distribution is 6, find the value of p.
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Find the mean salary of 20 workers of a factory from the table.
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The weights (in grams) of 30 oranges, picked at random from a basket of oranges are given below 90, 30, 45, 55, 65, 60, 50, 75, 70, 60, 70, 70, 60, 95, 85, 80, 35, 45, 40, 45, 55, 30, 110, 75, 100, 40, 60, 85, 40, 100
Construct a grouped frequency distrubution table with equal class intervals, one of them being 3040.
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Draw a histogram and frequency polygon (in the same diagram) for the following data :
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Draw a histogram and a frequency polygon from the following data :
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Calculate the difference between the upper limit of the class interval and the lower limit of the next class interval, i.e. 20 โ 21 = 1.
Half of the difference value is added to the upper limit of the class interval and half of the difference value is deducted from the lower limit of the class interval.
Exclusive series of the given inclusive series as follows:
Class Intervals Frequency
15.520.5 – 4
20.525.5 – 12
25.530.5 – 18
30.535.5 – 26
35.540.5 – 14
40.545.5 – 10
45.550.5 – 6
To draw frequency polygon, basically, the histogram is constructed and then the midpoints of the tops of rectangles in the histogram are marked. The marked midpoints are joined by using a foot rule to obtain the frequency polygon curve.
The weights (in kg) of 60 persons are given below. Find the mean weight of a person by (i) direct method (ii) deviation method.
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Draw a frequency polygon for the following data :
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Draw a frequency polygon for the following data:
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Draw a histogram and frequency polygon for the following distribution :
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The following table gives the distribution of students of two sections according to the marks obtained by them.
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons, compare the performance of the two sections
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Performance of section A is better than section B
The runs scored by two teams A and B in 7 overs in a cricket match are given.
Represent the data of both the teams on the same graph by frequency polygon.
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Following table shows the frequency distribution for the speeds of cars passing through a particular point on a highway.
Draw a histogram and a frequency polygon to represent the above data.
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Along the horizontal axis, we represent the class intervals on some suitable scale. The corresponding frequencies are represented along the vertical axis on a suitable scale.
We construct rectangles with class intervals as the bases and the respective frequencies as the heights.
Let us draw a histogram for this data and mark the midpoints of the top of the rectangles as B, C, D, E, F, G and H, respectively. Here, the first class is 3040 and the last class is 90100.
Also, consider the imagined classes 2030 and 100110 each with frequency O. The class marks of these classes are 25 and 105 at the points A and I, respectively.
Join all these points by dotted line.
Draw a histogram to represent the above data. Make a frequency polygon for given frequency table
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Draw a histogram to represent the following distribution.
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Following table gives the distribution of the marks obtained by the students of a class. Represent the data by frequency polygon.
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Draw the frequency polygon without constructing the histogram of the following observations.
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