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.
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).
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.
Modal lifetime of the components = 65.625 hours
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.
Modal monthly expenditure = ₹ 1847.83 (approximately)
Mean monthly expenditure = ₹ 2662.5
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.
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).
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.
Mode of the data = 4608.7 runs (approximately)
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.
Mode of the data = 44.7 cars