Univariate Data

New Zealand

Level 5

Lesson

While calculating the mean, median, mode and range can tell us a lot about a data set, these calculations can also be very powerful in comparing and contrasting two different data sets.

We also can benefit from examining the shape of the distribution of two sets of data when comparing them.

The number of minutes spent exercising per day for $10$10 days is recorded for two people who have just signed up for a new gym membership.

Person A: $45$45 $50$50 $50$50 $55$55 $55$55 $60$60 $60$60 $65$65 $65$65 $65$65

Person B: $20$20 $30$30 $45$45 $55$55 $60$60 $60$60 $65$65 $70$70 $70$70 $70$70

(a) Calculate the mean, median, mode and range for Person A

mode = $65$65

median = $57.5$57.5

mean = $57$57

range = $20$20

(b) Calculate the mean, median, mode and range for Person B

mode = $70$70

median = $60$60

mean = $54.5$54.5

range = $50$50

(c) Which person is the most consistent with their exercise?

Person A

(d) Which statistical measure supports your answer to part (c)?

The range. The smaller range for Person A indicates that the number of minutes they exercise each day is more consistent than that of Person B.

The range for Person B is more than double that of Person A, indicating more inconsistency in their exercise routine.

(e) Which person seems to train more overall?

Person B

(f) Which statistical measure(s) supports your answer to (e)?

The mode and median for Person B are both larger than for Person A.

While the mean for Person B is slightly lower than Person A, this is due to the negative skew of their data.

Overall, the larger mode and median for Person B indicates that they exercise for longer overall.

The beaks of two groups of bird are measured, in mm, to determine whether they might be of the same species.

Group 1 |
$33$33 | $39$39 | $31$31 | $27$27 | $22$22 | $37$37 | $30$30 | $24$24 | $24$24 | $28$28 |
---|---|---|---|---|---|---|---|---|---|---|

Group 2 |
$29$29 | $44$44 | $45$45 | $34$34 | $31$31 | $44$44 | $44$44 | $33$33 | $37$37 | $34$34 |

Calculate the range for Group 1.

Calculate the range for Group 2.

Calculate the mean for Group 1. Give your answer as a decimal.

Calculate the mean for Group 2. Give your answer as a decimal.

Choose the most appropriate statement that describes the set of data.

Although the ranges are similar, the mean values are significantly different indicating that these two groups of birds are of the same species.

AAlthough the ranges are similar, the mean values are significantly different indicating that these two groups of birds are not of the same species.

BAlthough the mean values are similar, the ranges are significantly different indicating that these two groups of birds are not of the same species.

CAlthough the mean values are similar, the ranges are significantly different indicating that these two groups of birds are of the same species.

D

The box plots drawn below show the number of repetitions of a $70$70 kg bar that two weightlifters can lift. They both record their repetitions over $30$30 days.

Which weightlifter has the more consistent results?

Weightlifter A.

AWeightlifter B.

BWhat statistical evidence supports your answer?

The mean.

AThe range.

BThe mode.

CThe graph is positively skewed.

DWhich statistic is the same for each weightlifter?

The median.

AThe mean.

BThe mode.

CWhich weightlifter can do the most repetitions of $70$70 kg?

Weightlifter A.

AWeightlifter B.

B

Derek planted some tomato seeds and two seeds sprouted. He puts Seedling A outside in the sun and Seedling B inside in the kitchen. The heights of the seedlings over time, in cm, are graphed below:

Loading Graph...

How many centimetres did Seedling A grow in the second week?

Complete the table below showing the increases in growth for both seedlings:

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7 Seedling A $3$3 cm $2$2 cm $\editable{}$ cm $\editable{}$ cm $2$2 cm $\editable{}$ cm $\editable{}$ cm Seedling B $\editable{}$ cm $\editable{}$ cm $\editable{}$ cm $\editable{}$ cm $\editable{}$ cm $\editable{}$ cm $\editable{}$ cm Which seedling appears to be growing more slowly?

Seedling A.

ASeedling B.

BWhich conditions seem to give optimum growth for a tomato seedling?

Growing inside in the kitchen.

AGrowing outside in the sun.

B

Plan and conduct surveys and experiments using the statistical enquiry cycle:– determining appropriate variables and measures;– considering sources of variation;– gathering and cleaning data;– using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets;– comparing sample distributions visually, using measures of centre, spread, and proportion;– presenting a report of findings