simple statistics?

Question

Q1 chosse 3 options which are correct
1) a symetric data set must have an odd number of modes
2) A symetric data set cannot have more than one mode
3) the median and interquartile range are measures of location in a set of data
4) the standard deviation and range are measures of dispersion in a set of data
5) interquartile ranges and more resistant to outliers in a set of data than is standard deviation
6) the mean is more resistant to outliers in a set of data than is median
7) In general, the mean is greater than median for right skew data
8) In general, the median is less than mean for right skew data

Q2 choose two options that give the upper quartile and upper adjacent value for data set below
2 4 8 6 3 9 8 11 20
a) 8.75 b) 9.5 c) 9.75 d) 10 e) 11 f) 14.75 g) 19.75 h) 20

Q3) The c.d.f of a continous random variable y is F(y) = y/(y+1) y>0 choose two options that give the median and upper quartile of y
a) 1/3 b) 1 c) 4/3 d) 2 e) 3 f) 4

Answer 1

Q1:
1, 2 are false: e.g. the set -1, -1, 0, 1, 1 has modes -1 and 1.
3 is false: the median is a measure of location but the IQR is a measure of dispersion.
4 is true.
5 and 6 are true (and related).
7 and 8 are true (and equivalent). For instance, consider the data set 0, 1, 8. The median is 1 and the mean is 3.
(Are you sure 8 wasn't meant to be the other way around, or for left skew data? It says exactly the same as 7, just very slightly rephrased.)

Q2. Sort the data set:
2 3 4 6 8 8 9 11 20
The first 8 is the median, the upper quartile is the median of 8 9 11 20 which is 10 and the upper adjacent value is 11.

Q3. For the median, F(y) = y/(y+1) = 1/2 => y = 1.
For the upper quartile, y / (y+1) = 3/4 => y = 3.