Connecting the Dots: questions with answers

The question "How many classmates enjoy drawing?" needs answers from a group. People in the group may give different answers. Collecting and counting these answers makes this a statistical question. Adding a number or asking only one person does not do this.

This question seeks only one person's preference at one time. That reply can be a data point, even if it is an opinion expressed in words. A statistical question seeks data across people or other cases where answers may differ.

The total is at least 4 × 3 = 12 and at most 4 × 29 = 116. Dividing by 4, the mean is at least 12 ÷ 4 = 3 and at most 116 ÷ 4 = 29. The exact mean depends on the individual amounts; it need not equal 16 or 29.

Every observation lies between 32 and 48 marks, so their mean must also lie in that interval. The claimed 27 is outside it. The midpoint 40 need not be the mean; all observations contribute to the mean.

Compare each height in Group A with 148 cm, the tallest height in Group B. The heights greater than 148 cm are 150 cm and 154 cm. The answer is 2. A higher mean does not mean that every student in Group A is taller than every student in Group B.

Recover each group's total by multiplying its mean by its size. The combined total is 360, with 20 observations, so the overall mean is 18. The unweighted midpoint 21 is incorrect here because the group sizes and means differ.

Sort the 6 values: 20, 21, 22, 28, 29, 60. The two central values are 22 and 28; their average is 25 kg. The later central value alone, the unsorted middle, and the midpoint of the extremes are different calculations.

Sort the five values and take the third. This gives 56 rupees. The original third value 33 reflects recording order, not size order. The mean 54.6 and midrange 50 are different summaries.

The filled entries are invented values, not recorded observations. An unchanged mean does not make them real. For tests taken, count the 5 recorded values, including zeros: 120 ÷ 5 = 24.

A verified unusual value is still part of the data. Keep it when reporting a mean of all observations. Here the mean is 16.5 and the median 8.5; report the appropriate summary with context rather than silently deleting the value.

Both drawings represent the same increase: 60 − 40 = 20. Dividing by 10 gives 2 drawing units, while dividing by 5 gives 4. The picture stretches; the numerical increase stays the same.

The first bar extends 30 rupees above the baseline, so it is one drawing unit long. The second is two drawing units long. Its value is 200 + 2 × 30 = 260 rupees.

Horizontal positions give the recorded values, and the number of dots at each value gives its frequency. These positions do not identify the student it represents. Student names attached to the dots provide that link. The mean summarises the values without identifying individual observations.

Both values belong to Week 1: 52 rupees for Ambagaon and 45 rupees for Belur. The cluster compares two groups for the same week. It gives neither a change within that period nor totals across all periods.

The increase compares counts for different subjects within each set. These categories are not successive times, so this increase does not describe growth over time. Comparing the two counts within one subject is a separate comparison.