NCERT Solutions
Class 10 - Mathematics - Chapter 13: STATISTICSExercise 13.2
Class 10 - Mathematics - Chapter 13: STATISTICS
Question. 1
The following table shows the ages of the patients admitted in a hospital during a year:
| Age (in years) | 5–15 | 15–25 | 25–35 | 35–45 | 45–55 | 55–65 |
|---|---|---|---|---|---|---|
| Number of patients | 6 | 11 | 21 | 23 | 14 | 5 |
Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
Answer:
Mode of the data = 36.8 years
Mean of the data = 35.37 years
Interpretation: The maximum number of patients admitted in the hospital are of age about 36.8 years (modal age), while on an average a patient admitted is about 35.37 years old (mean age).
Question. 2
The following data give the information on the observed lifetimes (in hours) of 225 electrical components:
| Lifetimes (in hours) | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 | 100–120 |
|---|---|---|---|---|---|---|
| Frequency | 10 | 35 | 52 | 61 | 38 | 29 |
Determine the modal lifetime of the components.
Answer:
Modal lifetime of the components = 65.625 hours
Question. 3
The following distribution gives the total monthly household expenditure of 200 families of a village:
| Expenditure (in ₹) | 1000–1500 | 1500–2000 | 2000–2500 | 2500–3000 | 3000–3500 | 3500–4000 | 4000–4500 | 4500–5000 |
|---|---|---|---|---|---|---|---|---|
| Number of families | 24 | 40 | 33 | 28 | 30 | 22 | 16 | 7 |
Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.
Answer:
Modal monthly expenditure = ₹ 1847.83 (approximately)
Mean monthly expenditure = ₹ 2662.5
Question. 4
The following distribution gives the state-wise teacher–student ratio in higher secondary schools of India:
| Number of students per teacher | 15–20 | 20–25 | 25–30 | 30–35 | 35–40 | 40–45 | 45–50 | 50–55 |
|---|---|---|---|---|---|---|---|---|
| Number of states / U.T. | 3 | 8 | 9 | 10 | 3 | 0 | 0 | 2 |
Find the mode and mean of this data. Interpret the two measures.
Answer:
Mode of the data = 30.6 students per teacher
Mean of the data = 29.2 students per teacher
Interpretation: In most states / U.T., the typical teacher–student ratio is about 30.6 (modal value), while on an average the ratio is about 29.2 students per teacher (mean value).
Question. 5
The following distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches:
| Runs scored | 3000–4000 | 4000–5000 | 5000–6000 | 6000–7000 | 7000–8000 | 8000–9000 | 9000–10000 | 10000–11000 |
|---|---|---|---|---|---|---|---|---|
| Number of batsmen | 4 | 18 | 9 | 7 | 6 | 3 | 1 | 1 |
Find the mode of the data.
Answer:
Mode of the data = 4608.7 runs (approximately)
Question. 6
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 following table:
| Number of cars | 0–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 | 60–70 | 70–80 |
|---|---|---|---|---|---|---|---|---|
| Frequency | 7 | 14 | 13 | 12 | 20 | 11 | 15 | 8 |
Find the mode of the data.
Answer:
Mode of the data = 44.7 cars