RANGE STANDARD DEVIATION AND VARIANCE WORKSHEET

Question 1 :

Find the range and coefficient of range of the following data

(i) 59, 46, 30, 23, 27, 40, 52, 35, 29

(ii) 41.2, 33.7, 29.1, 34.5, 25.7, 24.8, 56.5, 12.5

Solution

Question 2 :

The smallest value of a collection of data is 12 and the range is 59. Find the largest value of the collection of data.

Solution

Question 3 :

The largest of 50 measurements is 3.84 kg. If the range  is 0.46 kg, find the smallest measurement.

Solution

Question 4 :

The standard deviation of 20 observations is √5. If each observation is multiplied by 2, find the standard deviation and variance of the resulting observations.

Solution

Question 5 :

Calculate the standard deviation of the first 13 natural numbers.            Solution

Question 6 :

Calculate the standard deviation of the following data      

10, 20, 15, 8, 3, 4

Solution

Question 7 :

Calculate the standard deviation of the following data.

38, 40, 34, 31, 28, 26, 34

Solution

Question 8 :

Calculate the standard deviation of the following data

     x     3     8    13    18    23

     f     7    10    15    10    8

Solution

Question 9 :

The number of books bought at a book fair 200 students from a school are given in the following table.

Number of books              0       1        2       3        4

Number of students       35     64       68     18       15

calculate the standard deviation.

Solution

Question 10 :

The time (in seconds) taken by a group of people to walk across a pedestrian crossing is given in the table below.

Time (in sec)   5-10      10-15      15-20      20-25     25-30

No of people       4             8           15           12         11

Calculate the standard deviation.

Solution

Question 11 :

A group of 45 house owners contributed money towards green environment of their street. The amount of money collected is shown in the table below.

Amount          0-20   20-40   40-60    60-80    80-100

No of house      2         7          12          19           5 

Calculate the standard deviation.         Solution

Question 12 :

Calculate the variance of the following table.

x    2    4    6     8    10    12    14    16

f    4    4    5    15     8      5      4    5

Solution

Question 13 :

Find the variance of the following distribution

Solution

Question 14 :

The mean and standard deviation of 20 items are found to be 10 and 2 respectively. At the time of checking it was found that an item 12 was wrongly entered as 8. Calculate the correct mean and standard deviation.

Question 15 :

Mean of 100 items is 48 and their standard deviation is 10. Find the sum of all the items and the sum of the squares of all the items.

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