Hi! I need urgent help with this graph question!?

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.


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.

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)


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

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