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The mean of five positive integers is twice their median. If four of the integers are 3, 4, 6, 9 and median is 6, then find the fifth integer - Mathematics

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प्रश्न

The mean of five positive integers is twice their median. If four of the integers are 3, 4, 6, 9 and median is 6, then find the fifth integer

योग

उत्तर

Let the 5th positive integer be x

`bar(x) = (3 + 4 + 6 + 9 + x)/5`

= `(22 + x)/5`

Median = 6

Mean = 2 × median

`(22 + x)/5` = 2 × 6

22 + x = 60

x = 60 – 22

= 38

The fifth integer is 38.

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अध्याय 8: Statistics - Exercise 8.2 [पृष्ठ २८४]

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सामाचीर कलवी Mathematics [English] Class 9 TN Board
अध्याय 8 Statistics
Exercise 8.2 | Q 6 | पृष्ठ २८४

संबंधित प्रश्न

The marks of 10 students of a class in an examination arranged in ascending order is as follows:

13, 35, 43, 46, x, x + 4, 55, 61, 71, 80

If the median marks is 48, find the value of x. Hence, find the mode of the given data.


Find the mode and the median of the following frequency distribution:

x 10 11 12 13 14 15
f 1 4 7 5 9 3

In a school, 100 pupils have heights as tabulate below: 

 Height (in cm)  No. of pupils 
121 – 130 12
131 – 140 16
141 – 150 30
151 – 160 20
161 – 170 14
171 – 180 8

Find the median height by drawing an ogive.


Find the median and mode for the set of numbers:

2, 2, 3, 5, 5, 5, 6, 8 and 9 


The monthly income of a group of 320 employees in a company is given below:

Monthly income (thousands)  No. of employees 
6-7 20
7-8 45
8-9 65
9-10 95
10-11 60
11-12 30
12-13 5

Draw an ogive of the distribution on a graph paper taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph detemine: 

  1. the median wage. 
  2. number of employee whose income is below Rs. 8,500.
  3. If salary of a senior employee is above Rs. 11,500, find the number of senior employee in the company. 
  4. the upper quartile.

The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method.  Take the assumed mean as 45. Give your answer correct to 2 decimal places.

Number of patients 10 -  20 20 - 30 30 - 40 40 - 50 50 - 60 60 -  70
Number of Days 5 2 7 9 2 5

Find the mean of all numbers from 7 to 17.


Find the mode of the following frequency distribution: 

Hrs. Spent daily in studies 3 3.5 4 4.5 5 5.5 6 6.5
No. of students 8 7 3 5 10 6 3 4

Find the mean and the median of: 10,12, 12, 15, 15, 17, 18, 18, 18 and 19


An incomplete frequency distribution is given below

Variate Frequency
10 – 20 12
20 – 30 30
30 – 40 ?
40 – 50 65
50 – 60 45
60 – 70 25
70 – 80 18
Total 229

Median value is 46, the missing frequency is:


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