Lesson test: Describing a batch of numbers

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Describing a batch of numbers

1.[1p]
Seven salaries are 21, 23, 24, 26, 28, 30 and 210 thousand. What is the median, in thousands?

CorrectNot quite: 26

2.[2p]
For the same seven salaries, what is the mean, in thousands, to one decimal place?

CorrectNot quite: 51.7

3.[2p]
Which quantity does the sample mean minimise?

The sum of squared deviations $\sum (x_{i} - c)^{2}$

Correct

The sum of absolute deviations $\sum | x_{i} - c |$

The answer is: The sum of squared deviations $\sum (x_{i} - c)^{2}$

The largest single deviation $\max | x_{i} - c |$

The answer is: The sum of squared deviations $\sum (x_{i} - c)^{2}$

The number of points that differ from $c$

The answer is: The sum of squared deviations $\sum (x_{i} - c)^{2}$

4.[3p]
A batch is 2, 4, 4, 4, 5, 5, 7, 9. What is $s$ , the sample standard deviation with divisor $n - 1$ , to three decimal places?

CorrectNot quite: 2.138

5.[2p]
Adding 10 to every value in a batch leaves the sample standard deviation unchanged.

True

Correct

False

The answer is: True

6.[2p]
Match each summary to the partner it is normally quoted with.

Mean
Median
Geometric mean
Coefficient of variation

mean of the logarithms
interquartile range
standard deviation
$s / \overline{x}$

Show the answer

Mean: standard deviation Median: interquartile range Geometric mean: mean of the logarithms Coefficient of variation: $s / \overline{x}$

7.[3p]
Which of these are true of Anscombe's four datasets?

Select all that apply

They share the same means, variances, correlation and fitted line

Correct

One of them is an exact parabola with no linear relationship

Correct

In one of them a single point determines the whole slope

Correct

They differ in their sample sizes, which is what creates the effect

The answer is: They share the same means, variances, correlation and fitted line, One of them is an exact parabola with no linear relationship, In one of them a single point determines the whole slope

8.[2p]
Why is the median described as resistant while the mean is not?

Half the data can be replaced by arbitrary values before the median leaves the range of the rest

Correct

The median is always closer to the true population value

The answer is: Half the data can be replaced by arbitrary values before the median leaves the range of the rest

The median uses more of the information in the sample

The answer is: Half the data can be replaced by arbitrary values before the median leaves the range of the rest

The median has a smaller sampling variance for normal data

The answer is: Half the data can be replaced by arbitrary values before the median leaves the range of the rest

9.[2p]
Cavendish's quartiles are $Q_{1} = 5.295$ and $Q_{3} = 5.615$ . Below what value does the $1.5 \times IQR$ rule flag a point?

CorrectNot quite: 4.815

1.[1p] Seven salaries are 21, 23, 24, 26, 28, 30 and 210 thousand. What is the median, in thousands?

2.[2p] For the same seven salaries, what is the mean, in thousands, to one decimal place?

3.[2p] Which quantity does the sample mean minimise?

4.[3p] A batch is 2, 4, 4, 4, 5, 5, 7, 9. What is s, the sample standard deviation with divisor n−1, to three decimal places?

5.[2p] Adding 10 to every value in a batch leaves the sample standard deviation unchanged.

6.[2p] Match each summary to the partner it is normally quoted with.

7.[3p] Which of these are true of Anscombe's four datasets?

8.[2p] Why is the median described as resistant while the mean is not?

9.[2p] Cavendish's quartiles are Q1=5.295 and Q3=5.615. Below what value does the 1.5×IQR rule flag a point?

1.[1p]
Seven salaries are 21, 23, 24, 26, 28, 30 and 210 thousand. What is the median, in thousands?

2.[2p]
For the same seven salaries, what is the mean, in thousands, to one decimal place?

3.[2p]
Which quantity does the sample mean minimise?

4.[3p]
A batch is 2, 4, 4, 4, 5, 5, 7, 9. What is $s$ , the sample standard deviation with divisor $n - 1$ , to three decimal places?

5.[2p]
Adding 10 to every value in a batch leaves the sample standard deviation unchanged.

6.[2p]
Match each summary to the partner it is normally quoted with.

7.[3p]
Which of these are true of Anscombe's four datasets?

8.[2p]
Why is the median described as resistant while the mean is not?

9.[2p]
Cavendish's quartiles are $Q_{1} = 5.295$ and $Q_{3} = 5.615$ . Below what value does the $1.5 \times IQR$ rule flag a point?