Shape
Statistical Measures
Which one?
Chains?
Application
100
What is the shape of this histogram?
This is a bell shape.
100
What is used to measure the variability of the data set?
IQR and standard deviation.
100
In a symmetrical distribution the mean relates to the median in one of the ways, choose the correct one:
1) The Mean is greater than the Median.
2) The Mean is less than the Median.
3) The Mean is the same as the Median.
4) In the symmetrical distribution Median doesn't exist.
3)
The Mean is the same as the Median.
100
If you know that the appropriate measure of the center of the data set is mean, what must be true about the distribution?
A. The distribution is beautiful.
B. The distribution has uniform shape.
C. The distribution is symmetrical.
D. The distribution is represented by a histogram.
C. The distribution is symmetrical.
100
This histogram is showing the data on the number of toys donated by classes in a school for the fundraiser. One of the schools joined late. Their donation was 26 toys. What is going to happen to the mean of the data set after the new data point will be entered in the histogram?
The mean is going to increase.
200
What is the shape of this histogram?
This distribution is bimodal.
200
What is the appropriate measure of the center of the following data?
Median, because the distribution is skewed right.
200
What is greater, the mean or the median?
The mean is the same as the median, because the distribution is symmetrical.
200
Finish the statistical measures CHAIN by adding the appropriate variability measure:
Bell Shape > symmetrical > Mean > ___________
Bell Shape > symmetrical > Mean >STANDARD DEVIATION.
200
Two algebra teachers want to compare how their 7-student pilot groups performed on a midterm exam (scores out of 100).
Class A : 78, 82, 85, 85, 88, 92, 95
Class B : 60, 70, 85, 85, 90, 100, 100
In which class THE MEAN IS GREATER THAN THE MEDIAN?
Class A has the mean=86 and the median=85.
Class B has the mean=84 and the median =85.
Class A has the mean greater than the median.
300
What is the shape of this distribution?
This distribution is uniform.
300
What is appropriate measure of the center of the data?
Mean, because the distribution is symmetrical.
300
What is less, the mean or the median?
The mean is greater than the median.
300
The teacher said that for a data set IQR will be the most appropriate measure of variability. Based on the statement, what is true about the distribution? Choose all that applies:
a) The distribution is not symmetrical.
b) The most appropriate measure of the center is MEAN.
c) The most appropriate measure of the center is standard deviation.
d) The distribution has bell shape.
e) The most appropriate measure of the center is MEDIAN.
f) The distribution is skewed.
a), e), f).
300
Two algebra teachers want to compare how their 7-student pilot groups performed on a midterm exam (scores out of 100).
Class A: 78, 82, 85, 85, 88, 92, 95
Class B: 60, 70, 85, 85, 90, 100, 100
Which data set has greater variability?
Class B.
400
What is the shape of the distribution?
The distribution is skewed right.
400
What is the appropriate measure of variability of the data set?
Standard deviation, because the distribution is symmetrical.
400
What is greater, the mean or the median?
The median is greater than the mean.
400
Complete the STATISTICAL MEASURES chain:
___( add the shape) > NON symmetrical > ___(add the center measure) > IQR
SKEWED > NON symmetrical > MEDIAN > IQR
400
Two algebra teachers want to compare how their 7-student pilot groups performed on a midterm exam (scores out of 100).
Class A: 78, 82, 85, 85, 88, 92, 95
Class B: 60, 70, 85, 85, 90, 100, 100
If a school administrator values predictability and reliability (minimizing low-performing risk), which class do you recommend?
Class A.
500
What is the shape of the distribution?
It is not possible to determine the shape of the distribution, but this distribution is symmetrical.
500
If the outlier is removed, what is the most appropriate measure of variability of the data set?
Since with out the outlier the distribution has bell shape, the most appropriate measure of variability is standard deviation.
500
Compare to distributions. Which one has the mean greater than the median?
Red distribution has mean greater than the median. The distribution is skewed right, which causes the mean to increase. Black distribution is skewed left, so the mean is less than the median.
500
Complete the STATISTICAL MEASURES CHAIN for the distribution:
____(add the shape) > _____(symmetry) > ______(add the center measure) > ____(add the variability measure)
SKEWED RIGHT > NON SYMMETRICAL > MEDIAN > IQR
500
You are participating in the Brain Quest Game. Your team must accept an additional player. You have a choice from Kate and Barbara. Both are experienced players in Brain Quest. Their statistics, correctly answered questions, %, over the last ten games is given below:
Kate: Mean: 77, Median: 55, St. deviation: 13, IQR: 28
Barbara: Mean: 50, Median: 51, St. Deviation: 5, IQR: 4
Your team values reliability and predictability in players. Which player will be the best choice for your team?
Barbara has lower variability, so she meets the description. However, Kate is showing the overall performance higher than Barbara.