It says to compare shape, and values of this graph? - First of all I thought it was right skewed since lots of the value are on that side but answers say its left skewed!? I also don’t know how to calculate values from this exact graph to back up my centre, shape and spread. Please help!

Hi, @charlotteneedshelp.

**Shape:**

You say that distribution is right skewed when it has a “tail” on the right. This graph has the “tail” on the left so we can claim that it is left skewed.

**Mean:**

To calculate mean of this data it is common to use frequencies of the midpoints:

You can tell from the graph that 1 battery lasted a distance between 220 and 230km, 2 batteries lasted between 230 and 240km, 4 batteries lasted between 240 and 250km, and so on. For your calculations you can just use mid points: 225, 235, 245, 255, etc.

225 * 1 + 235 * 2 + 245 * 4 … etc, then you divide it by 69 (the total number of batteries: 1 + 2 + 4 + 6 + 11 + 9 + 12 + 15 + 9 + 2)

**Spread:**

You can see that difference between min (220km) and maximum (320km) is 100km, so you spread is 100km. You know that 99.7% of the data is located within +/- 3 standard deviations from the mean.

100/6 = 16.7km is your standard deviation.

This is great thank you - im just slightly confused about the spread part you talked about, where did the 99.7% come from and why is the 100km spread divided by 6 for the standard deviation?

This is a useful image of the normal distribution and standard deviation to keep in mind. That is a nature of standard deviation - to show spread of data. About 68.1% of data is located within +/- standard deviation, 95.2% of data within +/- 2 standard deviations and 99.6% of data (basically all your data) - within +/- 3 standard devations.

As you see total spread of data (Max - Min) contains 6 standard deviation (3 from each sides of mean).

You can also check it from tables of Z values:

You can see that when Z = 3 (your value X is 3 st.dev away from mean) that area under the graph between X and mean is 0.4987, or 49.87% of data is located between mean and value X for which Z = 3. Or 0.4897 * 2 = 0.9974 data located between values with Z = -3 and Z = 3