Advertisements
Advertisements
Question
Find the mean and variance for the following frequency distribution.
| Classes | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 |
| Frequencies | 5 | 8 | 15 | 16 | 6 |
Solution
Let assumed mean A = 25, class interval = 10
`y_i = (x_i - A)/h = (x_i - 25)/10`
| Class | Mid values | Frequency | yi | fiyi | yi2 | fiyi2 |
| 0 - 10 | 5 | 5 | −2 | −10 | 4 | 20 |
| 10 - 20 | 15 | 8 | −1 | −8 | 1 | 8 |
| 20 - 30 | 25 | 15 | 0 | 0 | 0 | 0 |
| 30 - 40 | 35 | 16 | 1 | 16 | 1 | 16 |
| 40 - 50 | 45 | 6 | 2 | 12 | 4 | 24 |
| Sum | - | - | - | 10 | - | 68 |
Mean `overline x = A + ((sumf_iy_i)/N) xx h`
= `25 + (10/50) xx 10`
= 25 + 2
= 27
Variance σ2 = `h^2/N^2 [N sumf_iy_i^2 - (sumf_iy_i)^2]`
= `100/2500 [50 xx 68 - 100]`
= `50/25[68 - 2]`
= 2 × 66
= 132
APPEARS IN
RELATED QUESTIONS
Find the mean and variance for the following frequency distribution.
| Classes | 0 - 30 | 30 - 60 | 60 - 90 | 90 - 120 | 120 - 150 | 150 - 180 | 180 - 210 |
| Frequencies | 2 | 3 | 5 | 10 | 3 | 5 | 2 |
Calculate the mean deviation from the median of the following frequency distribution:
| Heights in inches | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 |
| No. of students | 15 | 20 | 32 | 35 | 35 | 22 | 20 | 10 | 8 |
The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution:
| Number of calls | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Frequency | 14 | 21 | 25 | 43 | 51 | 40 | 39 | 12 |
Compute the mean deviation about median.
Calculate the mean deviation about the median of the following frequency distribution:
| xi | 5 | 7 | 9 | 11 | 13 | 15 | 17 |
| fi | 2 | 4 | 6 | 8 | 10 | 12 | 8 |
While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.
Calculate the mean, variance and standard deviation of the following frequency distribution.
| Class: | 1–10 | 10–20 | 20–30 | 30–40 | 40–50 | 50–60 |
| Frequency: | 11 | 29 | 18 | 4 | 5 | 3 |
