A Christmas Present for Everyone

Probability Level 2

There are eight people in a family. One of the members receives $x$ presents. Five members receive $x+4$ each and the rest only get $x-2$ each.

Consider the 8 numbers of presents received, and find $2 \times \mathrm{mode} - \mathrm{mean} - \mathrm{median}.$

The answer is 2.

4 solutions

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Michael Ng
Dec 24, 2014

The mode is $x+4$ . The median is also $x+4$ . The mean is: $\frac{x + 5(x+4) + 2(x-2)}{8} = x+2$ Therefore the answer is $2(x+4) - (x+2) -(x+4) = \boxed{2}$ .

there is a empirical formula for Mode is Mode=3Median-2mean. from this formula I'm solving 2.mode-mean-median= 5(median-mean) and finally getting answer is 10. Is that wrong?

Dhirendra Singh - 6 years, 5 months ago

The empirical formula is an approximation, and not a closed form solution.

Star Light - 6 years, 5 months ago

I also got the same result, 10.

Ayush Verma - 6 years, 5 months ago

I got it that way only, is it really wrong?

Aman Singh Pawaiya - 6 years, 5 months ago

What does mode mean?

Snehal Shekatkar - 6 years, 5 months ago

mode=data with highest frequency. mean=sum of all data divided by total count of data

Dhirendra Singh - 6 years, 5 months ago

just consider x,x+4 and x-2 as whole numbers and apply the formula of mean,median and mode.you will get your answer.2.

Mir Robab Warish Ali - 6 years, 5 months ago

Anna Anant
Jan 6, 2015

x + 4 Median = x + 4 Mean = (x + 2(x - 2) + 5(x + 4))/8 = (8x + 16)/8 = x + 2 So our value is 2(x + 4) - x - 2 - x - 4 = 2

Kshitij Gajapure
Jan 1, 2015

The mode is x+4, mean is x+2 & median is x+4 therefore ans is 2(x+4)-(x+4)-(x-2)=2

Gaurav Pandey
Dec 30, 2014

The mode is (x+4) and the median is also (x+4). Now mean is the average of all the observations, and it is (x+2). So, when we put the values in 2×mode-mean-median, we get 2×(x+4)-(x+2)-(x+4)=2

A Christmas Present for Everyone

The answer is 2.

4 solutions

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