Statistics 2

Question 1

What is a measure of location?

Answer 1

Single value that describes a position within a data set.

Question 2

If this value is describing the centre of the data?

Answer 2

This is a measure of central tendency.

Question 3

Mode/modal class?

Answer 3

Value/class that occurs most often.

Question 4

Median?

Answer 4

Middle value when all values ordered.

Question 5

Mean calculated by?

Answer 5

Sum of data values (∑x)/ number of data values (n)

Question 6

When is the mode an appropriate measure?

Answer 6

-Qualitative/quantitative data
-Single mode/bimodal data.

Question 7

Inappropriate to measure mode?

Answer 7

Each value only occurs once.

Question 8

Median usage?

Answer 8

Quantitative data only.

Question 9

Advantage of median vs mean?

Answer 9

Not affected by extreme values, so can be used in data with such values.

Question 10

Mean usage?

Answer 10

-Utilises all pieces of data, giving a true measure of the data.
-Used for quantitative data only.
-Is affected by extreme values.

Question 11

For data values of a frequency table, mean calculated by?

Answer 11

Frequency Density (Midpoint x Frequency) ∑xf/
Frequencies (∑f

Question 12

Median?

Answer 12

-Describes the middle of the data set, splitting the data into 2 50% halves.

Question 13

For effects on measure by a new data value, how is this evaluated?

Answer 13

Compare the previous value with the new one, if its larger, it increases etc.

Question 14

Lower quartile?

Answer 14

1/4 of the way through the data set.

Question 15

Upper quartile?

Answer 15

3/4s of the way through the data set.

Question 16

Percentiles?

Answer 16

-Split data into 100 parts.
(e.g. 10th percentile is 10/100 (1/10) of the way through the data).

Question 17

Calculate lower quartile for discrete data?

Answer 17

-n/4
-If integer, lower quartile halfway between this data point + next above.
-If not integer, round up and utilise this data point.

Question 18

Upper quartile of discrete data?

Answer 18

-3/4 of n
-If integer, upper quartile halfway between this data point + one above.
-If not integer, round up and utilise this data point.

Question 19

If data is presented in a group frequency table, how can medians, quartiles and percentiles be estimated?

Answer 19

Using process of linear interpolation.

Question 20

Why is there assumption involved in process of linear interpolation?

Answer 20

Assumed that data values are evenly distributed within each class/range.

Question 21

Lower + upper quartile + median in grouped continuous/cumulative frequency data calculation?

Answer 21

Q1: n/4th value

Q2: n/2th value

Q3: 3n/4th value

Question 22

Measure of spread?

Answer 22

Measure of how spread out data is.

Question 23

Range?

Answer 23

Difference between largest and smallest values of data set.

Question 24

IQR?

Answer 24

Difference between the upper quartile and lower quartile, Q3-Q1.

Question 25

Range qualities?

Answer 25

-Takes into account all data values. -Can be affected by extreme values.

Question 26

IQR qualities?

Answer 26

-Not affected by extreme values. -Only considers spread of the middle 50% of the data.

Question 27

If one data set has a higher IQR than another, what is the difference in data?

Answer 27

Higher IQR= increased variability in data (its more variable).

Question 28

Inter-percentile range?

Answer 28

Difference between values of two given percentiles.

Question 29

Frequently used IPR?

Answer 29

10-90th, as not affected by extreme values whilst still interpreting spread of 80% of data in the calculation.

Question 30

If asked to interpret the meaning of the value (like the IPR etc).

Answer 30

Just utilise the meaning of the measure (e.g. for mean, 50% of data larger, 50% smaller.)

Question 31

Variance?

Answer 31

-Another measure of spread of data. -Utilises the fact that each data point deviates from the mean by the amount of (the value-the mean) x-x-bar.

Question 32

Variance known as.

Answer 32

Mean of sqaures minus squares of mean.

Question 33

Variance eqns.

Answer 33

Refer to book.

Question 34

Standard deviation?

Answer 34

Square root of variance.

Question 35

Variance eqns for grouped frequency table.

Answer 35

Refer to book.

Question 36

If data in a grouped frequency table?

Answer 36

Using linear interpolation, you can calculate estimates for the variance and standard deviation of the data, with the midpoint of each class interval used in calculations.

Question 37

Coding?

Answer 37

Way of simplifying statistical calculations.

Question 38

Coding formula?

Answer 38

y=x-a b

Question 39

Why are values coded?

Answer 39

When coded, they create a new data value which is easier to work with.

Question 40

For the mean of coded data:

Answer 40

y-bar (coded mean)=x-bar (mean) - a/b (coding)

Question 41

For the mean of original data?

Answer 41

X-bar=by-bar + a

Question 42

For the standard deviation of the coded data?

Answer 42

sigma-y (coded standard deviation) =sigma-x (new standard deviation) /b

Question 43

Standard deviation of original data?

Answer 43

sigma-x=b x sigma-y.

Question 44

If asked to formulate code, and values decreased by 20% e.g, how is this interpreted.

Answer 44

Like normal 0.8(... etc.)