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a, b , c and d are four integers.
their mean is 8.
their mode is 7.
their median is 7.5.
find the four integers

Answer :

tylerflorida34638
7, 7, 8, 10 are the four integers

Explanation:
7 + 7 + 8 + 10 = 14 + 18 = 32 / 4 (to find mean) = 8

Mode means a number that occurs the most often, so 7 will be the answer

Median is the middle number, and that will be 7 and 8. To find median, you add up 7 and 8 together and divide the number by 2 to find the average, and that will be 7.5
varshamittal029

The four integers are 7, 7, 8, 10

What are the integers ?

Four integers are a, b, c, d

Mean = Sum of integers/Total number of integers

         = (a+b+c+d)/4

According to the question,

Mean = 8

i.e. (a+b+c+d)/4 = 8

⇒ a+b+c+d = 32 ......(1)

Median (for even no. of integers) = ([tex]\frac{n}{2}^{th} +(\frac{n}{2}+1)^{th}[/tex] term)/2

                                                       = (2nd+3rd term)/2

                                                       = (b+c)/2

According to the question,

Median = 7.5

i.e. (b+c)/2 = 7.5

⇒ b+c = 15  .....(2)

We know that, most frequent data is the mode.

So, mode = 7 means the number 7 occurs most frequently.

7 is not more than 2 times, because if 7 occurs 3 times, then 2nd & 3rd term will be 7 & median will be (7+7)/2 i.e. 7, so 3rd term must be larger than 7 to adjust the median value, which is 7.5

Then 1st two integers are 7 & 7

i.e. a = b = 7

Now, from (2), b+c = 15  

                    ⇒ 7+c=15

                    ⇒ c =15-7

                    ⇒ c = 8

Now, from (1) we get, a+b+c+d = 32

                                 ⇒ 7+7+8+d = 32

                                 ⇒ 22+d = 32

                                 ⇒ d = 32-22

                                 ⇒ d = 10

So, a = 7, b = 7, c = 8, d = 10

Learn more about mean, median, mode here :

https://brainly.com/question/14532771

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