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Question
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
| Literacy rate (in %) | 45 − 55 | 55 − 65 | 65 − 75 | 75 − 85 | 85 − 95 |
| Number of cities | 3 | 10 | 11 | 8 | 3 |
Solution
To find the class marks, the following relation is used.
`x_i = ("Upper class limit + Lower class limit")/2`
Class size (h) for this data = 10
Taking 70 as the assumed mean (a), di, ui, and fiui are calculated as follows:
| Literacy rate (in %) |
Number of cities fi |
xi | di = xi − 70 | ui = di/10 | fiui |
| 45 − 55 | 3 | 50 | −20 | −2 | −6 |
| 55 − 65 | 10 | 60 | −10 | −1 | −10 |
| 65 − 75 | 11 | 70 | 0 | 0 | 0 |
| 75 − 85 | 8 | 80 | 10 | 1 | 8 |
| 85 − 95 | 3 | 90 | 20 | 2 | 6 |
| Total | 35 | −2 |
From the table, we obtain
`sumf_i = 35`
`sumf_iu_i = -2`
`"Mean" barx = a+ ((sumf_iu_i)/(sumf_i))xxh`
= `70+(-2/35)xx(10)`
= `70-20/35`
= `70-4/7`
= 70 − 0.57
= 69.43
Therefore, the mean literacy rate is 69.43%.
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