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Statistics: CBSE Class 10 Mathematics practice questions

Practise 50 questions on Statistics, free, with an explanation for each answer.

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Sample questions

The class interval 45–6545\text{--}65 is shown on the strip. What is its class mark?

A strip from 45 to 65 with arrows from both ends meeting at the middle point marked with a question mark
  1. 2020
  2. 5555
  3. 110110
  4. 6565
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B. 5555

Class mark =upper limit+lower limit2=65+452=55=\dfrac{\text{upper limit}+\text{lower limit}}{2}=\dfrac{65+45}{2}=55. Writing 2020 gives the class width 65−4565-45. Writing 110110 forgets to divide the sum by 2, and 6565 just picks the upper limit.

The table shows the number of books read in a year by 20 students. Using the direct method, find the mean number of books read.

A table of five classes of books read, with frequencies and class marks 2, 6, 10, 14 and 18
  1. 1010
  2. 5.25.2
  3. 28.828.8
  4. 7.27.2
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D. 7.27.2

Products fxfx: 14, 42, 10, 42, 36, total ∑fx=144\sum fx=144. Mean =∑fx∑f=14420=7.2=\dfrac{\sum fx}{\sum f}=\dfrac{144}{20}=7.2. Traps: averaging the class marks without weights gives 1010, using lower limits instead of class marks gives 5.25.2, and dividing ∑fx\sum fx by the number of classes (5) gives 28.828.8.

The table shows the marks of 50 students. The step-deviation method is used with a=45a=45 and h=10h=10. Find the mean mark.

A table with columns marks, f, x, u equal to x minus 45 over 10, and f times u, with a totals row
  1. 45.2645.26
  2. 2.62.6
  3. 47.647.6
  4. 175175
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C. 47.647.6

xˉ=a+h∑fu∑f=45+10×1350=47.6\bar{x}=a+h\dfrac{\sum fu}{\sum f}=45+10\times\dfrac{13}{50}=47.6. Dropping hh gives 45.2645.26, dropping aa gives 2.62.6, and multiplying ∑fu\sum fu by hh without dividing by ∑f\sum f gives 175175.

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