Video: Measures of Central Tendency and Range

The ages of people who attend a parent-and-toddler group are recorded as follows: 2, 3, 29, 31, 4, 33, 2, 2, 1, 40, 3, 3, 24, 31. Calculate the mean age, giving your answer to one decimal place. Calculate the median age. Calculate the modal age. Calculate the range of ages. In this instance, given that none of the values would be considered outliers and taking into account the value of the range, which of the three measures of central tendency would be most informative of the whole data set.

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Video Transcript

The ages of people who attend a parent-and-toddler group are recorded as follows: two, three, 29, 31, four, 33, two, two, one, 40, three, three, 24, and 31. Calculate the mean age, giving your answer to one decimal place. Calculate the median age. Calculate the modal age. Calculate the range of ages. In this instance, given that none of the values would be considered outliers and taking into account the value of the range, which of the three measures of central tendency would be most informative of the whole data set?

We are given the ages of 14 parents and toddlers that attend the group. Eight of these are toddlers, whereas six are parents. The first part of the question asks us to calculate the mean. This is the sum of all the values divided by the number of values. The sum of the ages is equal to 208. Dividing this by 14 gives us 14.8571 and so on. As we need to round to one decimal place, the five is the deciding number. If this deciding number is five or greater, we round up. The mean age is therefore equal to 14.9.

To calculate the median of a data set, we firstly list the numbers in either ascending or descending order. And then we find the middle value. The ages written in ascending order go from one to 40 as shown. With a small data set like this, we can find the median by crossing off one number from either end. Repeating this five more times leaves us with two middle numbers of three and four. The median is the midpoint of these two values. As 3.5 is halfway between three and four, the median age is 3.5.

The mode or modal value is the value that appears the most. In this question, two and three appear three times. 31 appears twice. The other values only appear once. As two and three appear more frequently than any other age, the modal age is two and three. Out of our three measures of central tendency, the mean, median, and mode, only the mode can have more than one value.

The range of a data set can be calculated by subtracting the lowest number from the highest number. The highest number in our data set is 40, and the lowest is one. 40 minus one is equal to 39, so the range of ages is 39. The final part of our question asks us to look at the three measures of central tendency, the mean, median, and mode, and decide which would be the most informative for this data set. The mean value is usually affected by outliers. And in this case, we are told that there are no outliers. This suggests that the mean would be the most informative of the whole data set.

We can check this by studying our answers in more detail. Both the median and mode gave very small answers. This is because there were more toddlers than parents that attended the group. This has resulted in the median and mode being skewed towards the lower end of the data set. Therefore, these two measures did not give a good indication of the whole data set. The mean, on the other hand, of 14.9 factors in the adults and the children. This means that this is the best value of central tendency for the whole data set.

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