The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency f.
Daily pocket | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 | 19 - 21 | 21 - 23 | 23 - 25 |
Number of workers | 7 | 6 | 9 | 13 | f | 5 | 4 |
To find the class mark (\(x_i\)) for each interval, the following relation is used.
Class mark \((x_i)\) = \(\frac {\text{Upper \,limit + Lower \,limit}}{2}\)
Given that, mean pocket allowance,
Taking 18 as assured mean (a), \(d_i\), and \(f_id_i\) can be calculated as follows.
Daily pocket allowance (in Rs) | Number of children (\(f_i\)) | Class mark \(\bf{x_i}\) | \(\bf{d_i = x_i -150}\) | \(\bf{f_id_i}\) |
11 - 13 | 7 | -6 | -6 | -42 |
13 - 15 | 6 | 14 | -4 | -24 |
15 - 17 | 9 | 16 | -2 | -18 |
17 - 19 | 13 | 18 | 0 | 0 |
19 - 21 | \(f\) | 20 | 2 | 2\(f\) |
21 - 23 | 5 | 22 | 4 | 20 |
23 - 25 | 4 | 24 | 6 | 24 |
Total | \(\sum f_i\) = 44 + \(f\) |
|
| 2\(f\) - 40
|
From the table, we obtain
\(\sum f_i = 44 +f\)
\(\sum f_id_i = 2f - 40\)
Mean, \(\overset{-}{x} = a + (\frac{\sum f_id_i}{\sum f_i})\)
18 = \(18 + (\frac{2f - 40 }{44 + f})\)
0 =\(\frac{2f - 40 }{44 + f}\)
2\(f\) - 40 = 0
2\(f\) = 40
\(f\) = 20
Hence, the missing frequency f is 20.
Find mean of the following frequency table:
The following table shows the literacy rate (in percent) of 35 cities. Find the mean literacy rate.
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Literacy rate (in \%)} & 45-55 & 55-65 & 65-75 & 75-85 & 85-95 \\ \hline \text{Number of cities} & 3 & 10 & 11 & 8 & 3 \\ \hline \end{array}\]
The table below shows the daily expenditure on food of 25 households in a locality
Daily expenditure (in Rs) | 100 - 150 | 150 - 200 | 200 - 250 | 250 - 300 | 300 - 350 |
Number of households | 4 | 5 | 12 | 2 | 2 |
Find the mean daily expenditure on food by a suitable method.
In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.
Number of heartbeats per minute | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 |
Number of boxs | 15 | 110 | 135 | 115 | 25 |
Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
Consider the following distribution of daily wages of 50 workers of a factory
Daily wages (in Rs) | 500 - 520 | 520 -540 | 540 - 560 | 560 - 580 | 580 -600 |
Number of workers | 12 | 14 | 8 | 6 | 10 |
Find the mean daily wages of the workers of the factory by using an appropriate method.
‘दीवार खड़ी करना’ मुहावरे का वाक्य में इस प्रकार प्रयोग करें कि अर्थ स्पष्ट हो जाए।
Select from the following a statement which is not true about the burning of magnesium ribbon in air:
Analyze the significant changes in printing technology during 19th century in the world.
निम्नलिखित विषय पर संकेत बिंदुओं के आधार पर लगभग 120 शब्दों में एक अनुच्छेद लिखिए |
डिजिटल इंडिया
संकेत बिंदु -
डिजिटल इंडिया क्या है
डिजिटल होने के लाभ
सरकार द्वारा उठाए गए कदम