The median of x, 4x, 8x and 9x is = 24. What is the MEAN(average)? BASIC STATISTICS!

[@Hi-rw8vr]

22. The median is the middle value, however, as we have an even number of values, we take the mean of the middle 2. The mean of 4x and 8x is 12x/2 or 6x. This means 6x = 24 and x=4. From this, we can work put the exact values we have (4, 16, 32, 36). We add them together to get 88. Now as we have 4 values, we divide by 4, giving us 22.

[@robertstuart6645]

A very good problem in that it incorporates aspects of statistics coupled with the need to use fundamentals of algebra to complete the solution.

[@gavindeane3670]

(1+4+8+9)/4 is 11/2 so the mean is going to be (11/2)x. The median is going to be half way between 4x and 8x, which is 6x. So we have 6x = 24 therefore x=4 So mean = (11/2)×4 = 11×2 = 22

[@dazartingstall6680]

Nice. I used the same substitution of 4 for x that John did. Your method of reducing the mean to (11/2)x leaves less room for arithmetic errors.

[@dazartingstall6680]

(4x + 8x)/2 = 6x 6x = 24 x = 4 ∴ x + 4x + 8x + 9x = 4 + 16 + 32 + 36 = 88 88/4 = 22

[@Ayelmar]

Solved in my head, the men is 22. First, the median f an even number of observations is the mean of the two middle values. In other words (4x + 8x) / 2 = 6x, and if 6x = 24, then x = 24/6 = 4. Next, x + 4x + 8x + 9x = 22x. Then, since we know there are 4 values, and we know that x = 4, so 4/4 = 1, leaving just the 22 as the mean value.

[@russelllomando8460]

great explanation of the mid-point & average thanks for the fun.

[@pandurangaraonimmagadda9966]

(4x+8x)/2=24, 6x=24,x=4 mean=(4+16+32+36)/4=88/4=22

[@Poult100]

Thank you. Well explained!

[@Stylux-z1p]

10/26/2024 11:55 PM The mean is the average of a set of numbers: {10, 20, 30} --> Cardinality of the set is 3 -> 3 elements [10 + 20 + 30] / [3] = 60 / 3 = 20 -> mean of the set The median is the middle number in a sorted list of numbers. {2.5, 3.5, 4, 4.5, 5} since the cardinality of the set is odd -->5 The median will be one number -> 4 (the middle number) {1, 3, 5, 7} since the cardinality of the set is even --> 4 The median will be the average(mean) of the 2 middle numbers 3 and 5 --> [3 + 5] / [2] = 8/2 = 4 --> median of the set ------------------------------------------------------------------------------------------------ ordered Set {x, 4x, 8x, 9x} since the cardinality of the set is even --> 4 the median is formed by the average or mean of the 2 middle variables 4x and 8x --> [4x + 8x] / 2 = 24 12x / 2 = 24 2[12x / 2] = 2[24] 12x = 48 12x / 12 = 48 / 12 x = 4 Substitution of x = 4 in the set {x, 4x, 8x, 9x} --> {4, 16, 32, 36} proof: median of {4, 16, 32, 36} --> [16 + 32] / 2 = 48 / 2 = 24 --> The Median * ------------------------------------------------------------------------------------------------- The mean will be {4, 16, 32, 36} --> cardinality of the set is 4 [4 + 16 + 32 + 36] / 4 = 22 ---> The Mean *

[@dwaipayandattaroy9801]

4.36

[@capri102]

I definitely forgot all about this math. It's been forever since I did these problems 😂😂😂😂😂😂😂

[@bobhenson1433]

It may just be an anomaly, but adding the 4 integers 1,4,8,and 9 gives us 22, which was found to be the calculated mean. Hmmm?

[@dazartingstall6680]

It's a coincidence. x = 4, so when we divide 88 by 4 to get the mean, we're dividing by x.

[@christianbaughn199]

Hopefully this will demonstrate that it's just coincidence: The median of x, 4x, 8x and 9x is 30. What is the mean? (4x + 8x)÷2=30 12x÷2=30 6x=30 x=30÷6 x=5 Mean=(x+4x+8x+9x)÷4 =(5+20+40+45)÷4 =110÷4 =27.5 So the mean is 27.5, yet, 1+4+8+9=22

[@felipebriana8391]

Answer: 22

[@svanzijl75]

Easy if you know the definition of median. I did not, so did not know what to do.

[@jiyoungpark6233]

21.5...

[@josephlaura7387]

Mean = 22

[@loisjacobs2961]

Is it 22

[@tomtke7351]

¿¿ 11 ??

[@jald910]

22. 😀median is 6x so if 6x is 24 then x = 6. Total is 88 so mean is 88/4 = 22

[@osgubben]

You mean x=4

[@jald910]

@@osgubben yes I did. Right number in my head but wrote it down wrong. Not the first time. I still divided 88/4 not 6