Chapter 13 · Statistics

NCERT Class 10 Maths Exercise 13.2

All 6 questions of NCERT Class 10 Maths Exercise 13.2 (Statistics), in the book's order, each with its answer and a step-by-step solution.

1. Q1
   The following table shows the ​ages of the ​patients admitted in a hospital during a year. Find the mode and ​the ​mean of ​the data ​given above. Compare and interpret the two measures of ​central tendency.

   Ages of patients admitted

   Age (in years)	Number of patients
   5 - 15	6
   15 - 25	11
   25 - 35	21
   35 - 45	23
   45 - 55	14
   55 - 65	5

   Show answer

   Mode $\approx 36.8$ years and Mean $\approx 35.38$ years. The most common and the average ages are both about $36$ years, so a typical patient is in the mid-thirties.

   Step-by-step solution →
2. Q2
   The following data gives the information ​on ​the observed ​lifetimes (in hours) of 225 electrical components. ​Determine the modal lifetimes of ​the ​components.

   Observed lifetimes of electrical components

   Lifetimes (in hours)	Frequency
   0 - 20	10
   20 - 40	35
   40 - 60	52
   60 - 80	61
   80 - 100	38
   100 - 120	29

   Show answer

   Modal lifetime $=65.625$ hours.

   Step-by-step solution →
3. Q3
   The ​table below shows the daily expenditure on food ​of 25 households in ​a locality. Find ​the ​mean daily expenditure on food ​by a suitable method.

   Daily expenditure on food of 25 households

   Daily expenditure (in Rs)	Number of households
   100 - 150	4
   150 - 200	5
   200 - 250	12
   250 - 300	2
   300 - 350	2

   Show answer

   Mean daily expenditure on food $=$ Rs $211$.

   Step-by-step solution →
4. Q4
   The following distribution gives ​the state-wise ​teacher-student ratio in higher secondary schools ​of India. ​Find ​the mode ​and mean of ​this data. Interpret the two measures.

   State-wise teacher-student ratio in higher secondary schools of India

   Number of students per teacher	Number of states / U.T.
   15 - 20	3
   20 - 25	8
   25 - 30	9
   30 - 35	10
   35 - 40	3
   40 - 45	0
   45 - 50	0
   50 - 55	2

   Show answer

   Mode $\approx 30.6$ and Mean $\approx 29.2$ students per teacher. Most states have a ratio near $30.6$, while the average ratio across states is about $29.2$.

   Step-by-step solution →
5. Q5
   The given distribution shows the number of ​runs ​scored by some top batsmen of the world ​in ​one-day international cricket matches. Find the ​mode ​of ​the data.

   Runs scored by top batsmen in ODIs

   Runs scored	Number of batsmen
   3000 - 4000	4
   4000 - 5000	18
   5000 - 6000	9
   6000 - 7000	7
   7000 - 8000	6
   8000 - 9000	3
   9000 - 10000	1
   10000 - 11000	1

   Show answer

   $\text{Mode}\approx 4608.7$ runs.

   Step-by-step solution →
6. Q6
   A student noted the number of ​cars passing through a spot on ​a road for 100 periods ​each of 3 minutes and summarised it in the table ​given below. Find the mode of ​the ​data.

   Number of cars passing in 100 three-minute periods

   Number of cars	Frequency
   0 - 10	7
   10 - 20	14
   20 - 30	13
   30 - 40	12
   40 - 50	20
   50 - 60	11
   60 - 70	15
   70 - 80	8

   Show answer

   Mode $\approx 44.7$ cars per 3-minute period.

   Step-by-step solution →