# When is the sample median preferred to the sample mean?

## Homework Statement

i have a few easy questions but i need some help with them:
1)
a) Why do we need averages?
b) Which average can have more than one value?
c) Which average represents the value when the total of all the sample values is shared out equally?
d) Which average has the same number of values above it below it?
e) When is the sample median preferred to the sample mean?
f) When is the sample mode preferred to the sample mean?
g) When is the sample mean preferred to both the sample median and the sample mode?

2)
a) Why do we need measures of variation ?
b) What measure of variation is most useful in the case of: (i) a symmetrical distribution, (ii) a skew distribution'?
c) Think of an example of sample data where the range would be a misleading measure of variation.
d) Name the measure of variation associated with the: (i) sample mean, (ii) sample median, (iii) sample mode.
e) Name the average associated with the: (i) sample standard deviation, (ii) sample inter-quartile range, (iii) range.

## The Attempt at a Solution

1)
a) to analyse the data
b) when there's more than one dependent variable
c) i dont know
d)i dont know
e)when there's numerical data
f) when theres discrete data
g) when the histogram is symmetrical

2)
a) i dont know
b) i) mean/standard deviation ii) median/interquartile range
c) i dont know
d) i dont know
e) i dont know

any help would be very appreciated.
thank you.

## Answers and Replies

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EnumaElish
Science Advisor
Homework Helper
1)
a) to analyse the data: WOULD "SUMMARIZE" BE A BETTER WORD THAN "ANALYZE"?
b) when there's more than one dependent variable: NO. I AM INCLINED TO SAY "MOVING AVERAGE" BUT THAT'LL DEPEND ON THE CONTEXT.
c) i dont know: CAN YOU THINK OF AN EXAMPLE?
d)i dont know: DITTO
e)when there's numerical data: NO -- IT HAS TO DO WITH SYMMETRY AND OUTLIERS
f) when theres discrete data: NO -- IT HAS TO DO WITH "NUMERICAL DATA" VS. _________ ("DISCRETE" CAN ALSO BE NUMERICAL; E.G., INTEGER NUMBERS ARE DISCRETE)
g) when the histogram is symmetrical: THIS WILL FOLLOW FROM E AND F ABOVE

2)
a) i dont know: TO SUMMARIZE EXPANSIVENESS OF DATA?
b) i) mean/standard deviation ii) median/interquartile range: MEAN AND MEDIAN AREN'T MEASURES OF VARIATION. (THEY ARE MEASURES OF LOCATION.)
c) i dont know: THINK "OUTLIER(S)"
d & e) i dont know: D & E ARE "MATCHING PAIRS," YOU NEED TO MAKE THE RIGHT MATCHES.

Last edited:
i dont undrerstand what they mean by measures of vairation ??

D H
Staff Emeritus
Science Advisor
i dont undrerstand what they mean by measures of vairation ??
Consider these two sets of numbers:
Set #1 : {2,1,2,2,2,3,2,2}
Set #2 : {3,1,2,2,0,2,4,2}
Both sets have the same mean, median, and mode. The second set exhibits a lot more deviations from the mean than does the first set.

so why do we need measures of variation, i'm sorry i just dont understand.

and i still dont know how to do question 2

:(

CompuChip
Science Advisor
Homework Helper
For a), D H practically gave you the answer: because they give us some information we would otherwise miss.
For c): How is the range determined? Can you think, for example, of a set with a very wide range but very small variations?