Let's talk about something you are interested in-grades. You remember after each exam you were interested in knowing the results and what it would mean for your grade in the course. Now let look at grades from the instructor's side. Below you will find the complete data set for the first test in a recent course. There were 52 students that received the following scores on their exams.

While this may be useful to you for some purposes, but I suspect you were not interested in studying the entire class results. In the past I have had students ask: What is the average grade? How many students got As? What score did most students get? How many students did better than I did? What were the highest and lowest scores? For each of these questions we do not need to show the entire data set as our answer. In answering these questions there would be an interest in summarizing the data, which is where descriptive statistics comes in. Descriptive statistics offers us a way of summarizing large sets of data, and although in general we will not be able to reproduce the exact data from the summary statistics, they do offer us some insight into the underlying data.

Student	Grade	Student	Grade	Student	Grade	Student	Grade
1	91.983	14	97.531	27	96.8659	40	89.0001
2	91.7597	15	98.2979	28	76.2859	41	76.5876
3	87.9158	16	70.4242	29	99.6804	42	93.3512
4	77.0586	17	72.6251	30	87.6299	43	88.82
5	98.7479	18	86.9584	31	89.6395	44	77.4919
6	79.8029	19	95.2241	32	85.6969	45	94.7336
7	80.5968	20	91.9544	33	95.2098	46	75.4139
8	77.8953	21	80.2882	34	71.9719	47	86.5368
9	96.1051	22	77.2291	35	92.3448	48	93.7865
10	74.1581	23	93.1482	36	74.4269	49	73.8672
11	83.152	24	75.1727	37	82.7137	50	75.7028
12	91.7678	25	87.5282	38	77.8714	51	73.415
13	78.1368	26	80.501	39	71.828	52	74.7755

Two features of data sets such as this that have attracted the most interest, and which we will examine here, are Central Tendency and Variation. Let's return to our initial questions: What is the average grade? and What score did most students get? are questions concerning Central Tendency. How many students did better than I did? What were the highest and lowest scores? and How many students got As? are questions concerning variability. We will look at each of these and then move to a discussion of distributions.

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