Question

what is the means of the mode and median of the data given below 8,7,5,4,9,1,3,7,6,5,2,1,6,3,9,8,4,6​

Answer 1

Answer:

Correct answer is 5.75

Step-by-step explanation:

•Finding Mode:

Mode is the most repeated number in the data set. so

Mode=6

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•Finding Median:

The median is found by ordering the given set from lowest to highest and finding the exact middle.

ordered set of given data is:

1,1,2,3,3,4,4,5,5,6,6,6,7,7,8,8,9,9

Since it is an even number of numbers, we have to add the two middles and divide by 2. Then result will be the median.

(5+6)/2=5.5

Median= 5.5

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•Finding Mean of Mode and Median:

Mean= Sum of objects/Total no of objects

Mean=(Mode+Median)/2

Mean= (6+5.5)/2

Mean= 11.5/2

MEAN= 5.75

Hence, the mean of the mode and median of the data given is 5.75

Answer 2

Given,

Data = $\[8,7,5,4,9,1,3,7,6,5,2,1,6,3,9,8,4,6\]$

Solution,

Mean of the data,

$\[ = \frac{{\sum n }}{n}\]$

$\[ = \frac{{8 + 7 + 5 + 4 + 9 + 1 + 3 + 7 + 6 + 5 + 2 + 1 + 6 + 3 + 9 + 8 + 4 + 6}}{{18}}\]$

$\[ = \frac{{94}}{{18}}\]$

$\[ = 5.22\]$

Mode of the data,

Arrange the data in ascending order.

$\[1,1,2,3,3,4,4,5,5,6,6,6,7,7,8,8,9,9\]$

In the given data 6 is repeated 3 times which is maximum so mode of the data is 6.

Median of the data,

$\[median = \frac{{2mean + {\mathop{\rm mode}\nolimits} }}{3}\]$

$\[\begin{array}{l} = \frac{{2 \times 5.22 + 6}}{3}\\ = \frac{{10.44 + 6}}{3}\\ = \frac{{16.44}}{3}\\ = 5.48\end{array}\]$

Hence the mean, mode and median of the data are $\[{5.22}\]$, $\[6\]$, and $\[5.48\]$.