Construct histograms and describing histograms

1. Histograms

2. Start with a set of data 43, 48, 54, 32, 69, 77, 72, 60, 42, 33, 37, 78, 67, 63, 59

3. Rearrange your data from least to greatest 32, 33, 37, 42, 43, 48, 54, 59, 60, 63, 67, 69, 72, 77, 78

4. Create the horizontal axis Begin with minimum. Next determine your scale. General rule is to find the range (maximum – minimum) and divide by 7. Take this value and round off to the nearest integer and this will be our scale. In our example: (78-32) = 46 divided by 7 = 6.57, round to 7 for our scale. 32 39 53 67 81

5. 3. The vertical axis represents your frequency (how many observations fall into each bar we are going to create) 32 39 53 67 81

6. Now create your bars. The first bar will contain any data greater than or equal to 32 and less than (not equal to) 39. 39 is the smallest value that goes into the second bar. 32, 33, 37, 42, 43, 48, 54, 59, 60, 63, 67, 69, 72, 77, 78 32 39 53 67 81

7. Second bar will contain values equal to 39 and less than 46 32, 33, 37, 42, 43, 48, 54, 59, 60, 63, 67, 69, 72, 77, 78 32 39 53 67 81

8. and finish: 32, 33, 37, 42, 43, 48, 54, 59, 60, 63, 67, 69, 72, 77, 78 32 39 53 67 81

9. Now we can describe our histogram The three most important things are: 1. shape 2. center 3. spread Others that you may possibly use are: min/max gaps outliers peaks

10. Shape: Our distribution will be labeled one of the following 1. Symmetric 2. Skewed (right or left depending on tail direction) 3. Neither Symmetric Skewed left 32 39 53 67 81

11. Center: We can either use mean or median. We don’t want to use mode since in may not be in the middle. The median is generally easier since we can count from each side until we get to the middle. 32 39 53 67 81

12. Spread: Tells us how spread out our data is. Not always needed unless we compare multiple sets of data. For instance if we have a histogram comparing male and female test scores and want to know which gender had the larger range of values on the test. 32 39 53 67 81