Interpreting Statistics

Question 1

What does a box plot show in relation to data?

Answer 1

The shape,
Central Tendency,
Variability of the data

Question 2

What the best conditions to use a boxplot?

Answer 2

When sample size is greater than 20

Question 3

Can box plots be used to identify outliers?

Answer 3

Yes

Question 4

What is the coefficient of variation? (CoefVar)

Answer 4

Describes the variation in the data compared to the mean

Question 5

How do you interpret the variation of data?

Answer 5

The larger the variation, the greater the spread in the data.

Question 6

What are quartiles?

Answer 6

Values that divide the sample of ordered data into four equal parts

Question 7

What does the 25th percentile mean?

Answer 7

It indicates that 25% of the data are less than or equal to this value

Question 8

How do you calculate the Interquartile Range (IQR)

Answer 8

Quartile 3 - Quartile 1

*Descriptive stats in excel will not do this

Question 9

What does a histogram do?

Answer 9

Divides the sample values into many intervals and represents the frequency of data values in each interval with a bar

Question 10

How can you tell if the data is normally distributed?

Answer 10

If the data is symmetric (spike in the middle with equal tails left and right)
This can be indicated by a curve
Bell-shaped

Question 11

What charts can display skewness easily?

Answer 11

Histograms and boxplots

Question 12

What is kurtosis?

Answer 12

It indicates how the peak and tails of a distribution differ from the normal distribution

Question 13

What does a kurtosis value of 0 mean?

Answer 13

Baseline:

Value of 0 indicates that the data follows the normal distribution perfectly.

Question 14

What does a positive kurtosis value mean?

Answer 14

This indicates that the distribution has heavier tails and a sharper peak than normal distribution.

Question 15

What does a negative kurtosis value mean?

Answer 15

This indicates that the distribution has lighter tails and a flatter peak than the normal distribution.

Question 16

What can the maximum value be used for?

Answer 16

To identify any possible outliers or data entry errors. (especially if the maximum is very high compared to the rest of the data)

Question 17

How can you interpret the mean?

Answer 17

• Used as a standard measure of the centre of the distribution of the data
• Measures central tendency
• If data is symmetric mean and median are similar

Question 18

What is the median?

Answer 18

Midpoint of the data set.

Half of the data is below the median and the other half is above the median

Question 19

How can you interpret the median?

Answer 19

• Measures central tendency

- Outliers affect the median less than they affect the mean, useful for comparison

Question 20

What is the mode?

Answer 20

The value/number in the data set that occurs most frequently

There can be multiple modes so make sure to check

Question 21

How can you interpret the mode(s)?

Answer 21

• Can be used to identify problems in the data
• If the data has two modes it is called bimodal
• Data has more than two modes, it is called mutli-modal
• Mode can be used with mean and the median to provide an overall view of the data

Question 22

How can you interpret the range?

Answer 22

A large range indicates greater dispersion in the data

A small range indicates that there is less dispersion in the data

Question 23

What does SE stand for?

Answer 23

Standard error of the mean

Question 24

What does standard error of the mean do?

Answer 24

Estimates the variability between sample means
(so if you took repeated samples of the same population you can estimate the mean)
(The SD only measures the variation in a single sample)

Question 25

How can you interpret the SE mean?

Answer 25

A smaller value of the SE indicates a more precise estimate of the population mean. -A larger sample size results in a smaller SE of the mean- more precise

Question 26

What is skewness?

Answer 26

Is the extent to which the data are not symmetrical

Question 27

How can you interpret the skewness?

Answer 27

- Data more symmetrical, = skewness value close to or at 0 - A positive skew/ right skewed means the value is over 0 and positive - A negative skew/left skewed means the value is under 0 and negative

Question 28

What is Standard deviation?

Answer 28

-Most common measure of dispersion, how spread out the data are about the mean

Question 29

How can you interpret the SD?

Answer 29

- A higher SD value indicates greater spread in the data | - Normal distribution= means that 68% of the values fall within the one standard deviation

Question 30

How much of the data should fall within two standard deviations?

Answer 30

95% of the data

Question 31

How much of the data should fall within three standard deviations?

Answer 31

99.7% of the data

Question 32

What is variance?

Answer 32

The variance measures how spread out the data are about their mean. The variance is equal to the standard deviation squared

Question 33

How can you interpret the variance?

Answer 33

- Squared quantity (make sure you have squared units) | - The greater the variance, the greater the spread in the data