Univariate Data

Lesson

Often, instead of calculating statistics from a data set, we want to be able to calculate them from a statistical graph.

In the next few examples we'll take a look at how to calculate the mean, median, mode and range from a graph.

The back-to-back stem and leaf graph below shows the ages of people, in years, at a BBQ.

(a) How many people were at the BBQ?

By counting all the numbers in the "leaves" section we can see that there were $19$19 people at the BBQ.

(b) How old is the oldest person?

The oldest person is in the last row, right at the end of the line of data. So the oldest person is $58$58 years old.

(c) How old is the youngest person?

The youngest person is in the first row, right at the beginning of the line of data. So the youngest person is $10$10 years old.

(d) What is the range of the ages?

Using our answers from (b) and (c) we can say that the range is $58-10=48$58−10=48 years

(e) What is the mode of these ages?

Looking at the data, we can see it is bimodal, with each of $35$35 and $41$41 appearing twice.

(f) Calculate the mean age.

mean = $\frac{686}{19}$68619

mean=$36.12$36.12

(g) Calculate the median age.

If there are $19$19 people and we arranged them in order from youngest to oldest, which person would be in the middle? The $10$10th person. Counting $10$10 people on from either the youngest or the oldest person, we find that the $10$10th person is $36$36 years old.

The dot plot below shows the number of goals scored by a forward in the game of football.

(a) How many games did this player compete in?

Since each dot represents one game, if we count the dots we see he played $37$37 games.

(b) What was the most frequent number of goals scored?

Just like in our first example, we can see that the player scored $1$1 goal $9$9 times, and $4$4 goals $9$9 times. So this data is bimodal with modes of $1$1 and $4$4.

(c) What was the mean number of goals scored?

mean =$\frac{0\times1+1\times9+2\times8+3\times7+4\times9+5\times3}{37}$0×1+1×9+2×8+3×7+4×9+5×337

mean = $2.62$2.62

(d) Calculate the median for her set of data.

In a data set of $37$37 points, the middle number is the $19$19th score. If we count from the first dot to the $19$19th dot we arrive at a dot in the $3$3 column. So our median is $3$3.

From the frequency polygon shown:

Find the number of scores.

Calculate the sum of the scores.

Calculate the mean of the scores, correct to 2 decimal places.

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